Question

If the straight lines 3x – 5y = 7 and 4x + ay + 9 = 0 are perpendicular to one another, find the value of a.

Answer 1

3x - 5y = 7

`=> 5y = 3x - 7`

`=> y = 3/5 x - 7/5`

⇒ Its slope = `3/5`

4x + ay + 9 = 0

⇒ ay = -4x - 9

`=> y = (-4)/a x - 9/a`

⇒ Its slope = `(-4)/a`

Since lines are perpendicular to each other,

`3/5 xx (-4)/a = -1 => 3/5 xx 4/a = 1 => 4/a =    5/3`

`=> a = (4xx3)/5 = 12/5`